Least Squares Regression Line (LSRL)
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Key Questions

Answer:
All this means is the minimum between the sum of the difference between the actual y value and the predicted y value.
#min sum_(i=1)^n(y_ihaty)^2# Explanation:
Just means the minimum between the sum of all the resuidals
#min sum_(i=1)^nhatu_i^2# all this means is the minimum between the sum of the difference between the actual y value and the predicted y value.
#min sum_(i=1)^n(y_ihaty)^2# This way by minimizing the error between the predicted and error you get the best fit for the regression line.

Equation for leastsquares linear regression:
#y = m x + b# where
# m = (sum(x_iy_i)  (sum x_i sum y_i)/n)/(sum x_i^2 ((sum x_i)^2)/n)# and
#b = (sum y_i  m sum x_i)/n# for a collection of
#n# pairs#(x_i,y_i)# This looks horrible to evaluate (and it is, if you are doing it by hand); but using a computer (with, for example, a spreadsheet with columns :
#y, x, xy, and x^2# ) it isn't too bad. 
The primary use of linear regression is to fit a line to 2 sets of data and determine how much they are related.
Examples are:
2 sets of stock prices
rainfall and crop output
study hours and grades
With respect to correlation, the general consensus is:
Correlation values of 0.8 or higher denote a strong correlation
Correlation values of 0.5 or higher up to 0.8 denote a weak correlation
Correlation values less than 0.5 denote a very weak correlation\f 
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